Recognizing heterogeneous sequences by rational type expression

We summarize a technique for writing functions which recognize types of heterogeneous sequences in Common Lisp. The technique employs sequence recognition functions, generated at compile time, and evaluated at run-time. The technique we demonstrate extends the Common Lisp type system, exploiting the theory of rational languages, Binary Decision Diagrams, and the Turing complete macro facility of Common Lisp. The resulting system uses meta-programming to move an Omega(2^n) complexity operation from run-time to a compile-time operation, leaving a highly optimized Theta(n) complexity operation for run-time.